I want to ask a question to a specific user on Islam.SE, but I don't have the reputation to create or participate in chat.
How can I ask my question to this user?
Here on meta the rules are a little different but fundamentally we are not a chat site. We are a Q&A site and privileges like chat are earned by creating quality questions and answers.
If your question is on-topic at one of the varies SE sites, go ahead and post it there. This does not require any reputation and if it is a good question, will help you earn other privileges.
If your question is a personal one that can only be answered by a single user, you are out of luck. That is not something this site is for. Even if you had access to chat you wouldn't be able to directly message another users unless they were also active in the same chat.
Basically, if you have a question, ask it as a question on the appropriate site. Don't worry about chat as that is not what the site is focused on.
Ironically, your question shows a few good results from the site having chat be a rep-locked privilege and having no easy way to DM someone.
If you have a question that is on-topic for Islam.SE, then you should ask it there as a question. Chat isn't for bypassing the question-asking process to target a single user with a request. Nobody is going to help you work around the entire point of this site, if that is your intent. If you have a question, ask it the way the site wants you to. The person you are trying to reach is a moderator of that site, if you post a question, it seems likely that they'll see it.
When you have <20 rep you have no way to initiate or participate in chats on your own. The only exception is under your own Q/A.
The only way it's possible is if a mod or RO specifically whitelists you into a room. There's no good way that I'd recommend to contact one of those people however.
The easiest way, is the intended way: by gaining rep.
With 5 rep, you could simply comment on a post and ask your question (assuming it is relevant to their post). You can gain more than 5 rep by getting a single upvote on a Q or A that you post or from several approved edits.
With 20 rep, you could go to the site's main chatroom and see if you can ping them there (if you have 20 rep). Or combine it with a comment to see if that person is willing to create a room for you and them to talk which you can then join.
@
before a person's username you can notify them that you have responded in a comment.)